Stochastic analysis of coupled heave-roll ship motion using the domain decomposition chaotic radial basis function

The effect of uncertainties in the roll and heave natural frequencies as well as in the wave amplitude are investigated on the stochastic parametric ship roll motion using the Domain Decomposition Chaotic Radial Basis Function, which is a novel computational scheme proposed here. These uncertain parameters are represented by random variables with arbitrary distribution which in fact constitute the random input of the stochastic model of roll motion. The random input is divided into a number of random subdomains, in which the stochastic heave and the roll motions are represented using the proposed method. By applying the stochastic heave and roll responses in a nonlinear coupled model of heave and roll motions and subsequently employing a Galerkin projection, the deterministic set of equations governing the stochastic parametric roll response in each random domain are obtained. Through presenting various numerical examples, it is shown that the uncertainty in the system and loading parameters can considerably affect the prediction of the statistics of the parametric ship roll response. Further, the numerical results of the method are compared with those of the Monte Carlo simulation method and a very good agreement is obtained while the computational cost is considerably saved.